Nonequilibrium effects on one-norm geometric correlations and the emergence of a pointer-state basis in the weak- and strong-coupling regimes

Correlations in the open quantum systems manifest a rich phenomenology under the influence of various physical sources of noise. We theoretically study the dynamics of quantum correlations and their classical counterparts in a two-qubit system, measured by one-norm geometric quantifiers. We consider both qubits are initially prepared in the arbitrary $X$-type states and locally subjected to nonequilibrium dephasing environments with non-Markovian and nonstationary statistical features. We then explore the effects of nonequilibrium on the abrupt changes in the evolution of geometric correlations in the weak- and strong-coupling regimes. Particularly, in the weak-coupling regime, we show that the environmental nonequilibrium feature can efficiently control the appearance of double-sudden transitions and the decay rate in geometric quantum correlation dynamics. However, in the strong-coupling case, we show that the nonequilibrium nature can prolong the interval for the frozen quantum correlation and suppresses the number of multiple sudden changes in its decay rate. Moreover, the abrupt change from decay to a constant regime in classical correlation evolution reveals the emergence of the pointer-state basis. We show that the pointer-state basis appearance can be retarded in the weak-coupling case when the environment deviates from equilibrium. However, in a strong-coupling regime, we observe the metastable pointer-states basis characterized by multiple, successive sudden transitions in classical correlation dynamics. Remarkably, we unveil that the nonequilibrium feature may suppress the apparition of the metastable pointer-states basis.

Figure 1

Time-evolution of (a) correlation functions $|{\alpha }_1\left(t\right)|$ (purple curves), $|{\alpha }_2\left(t\right)|$ (pink curves), $|{\alpha }_3\left(t\right)|$ (black solid curve); (b) quantum correlations (blue curves); and (c) classical correlations (red curves) for different values of the nonequilibrium parameter $a=0, a=\pm 0.6, a=\pm 1$ (represented by dotted, dashed, solid curves in all cases), in the weak-coupling regime ($\epsilon /\lambda =0.8$) with damping rate $\kappa =\lambda$ and initial correlation parameters $c_1=1, c_2=0.50, c_3=0.30, c_4=0.10$, and $c_5=0.20$. The inset in panel (a) shows the longer-time dynamics of quantum correlations. In panel (c), the vertical gray lines manifest the sudden transition times for classical correlations associated with the emergence of the pointer-state basis.

Figure 2

Time-evolution of (a) correlation functions $|{\alpha }_1\left(t\right)|$ (purple curves), $|{\alpha }_2\left(t\right)|$ (pink curves), $|{\alpha }_3\left(t\right)|$ (black solid curve); (b) quantum correlations (blue curves); and (c) classical correlations (red curves) for different values of the nonequilibrium parameter $a=0, a=\pm 0.6, a=\pm 1$ (represented by dotted, dashed, solid curves in all cases), in the strong-coupling regime ($\epsilon /\lambda =4$) with damping rate $\kappa =\lambda$ and initial correlation parameters $c_1=1, c_2=0.50, c_3=0.30, c_4=0.10$, and $c_5=0.20$.